We obtain hardness results and approximation algorithms for two related geometric problems involving movement. The first is a constrained variant of the k-center problem, arising from a geometric client-server problem...
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We obtain hardness results and approximation algorithms for two related geometric problems involving movement. The first is a constrained variant of the k-center problem, arising from a geometric client-server problem. The second is the problem of moving points towards an independent set. (C) 2011 Elsevier B.V. All rights reserved.
We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs it...
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ISBN:
(纸本)9783540755197
We present a new algorithm that can output the rank-decomposition of width at most k of a graph if such exists. For that we use an algorithm that, for an input matroid represented over a fixed finite field, outputs its branch-decomposition of width at most k if such exists. This algorithm works also for partitioned matroids. Both these algorithms are fixed-parametertractable, that is, they run in time O(n(3)) for each fixed value of k where n is the number of vertices / elements of the input. (The previous best algorithm for construction of a branch-decomposition or a rank-decomposition of optimal width due to Oum and Seymour [Testing branch-width. J. Combin. Theory Ser. B, 97(3) (2007) 385-393] is not fixed-parametertractable).
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